Current measurements of the coupling constants of the 125 GeV Higgs boson at the LHC Run 2 [1]}, [2]} show that the properties of the discovered Higgs boson are similar to those predicted in the SM.
Theoretically, this situation can be realized in the so-called alignment limit,
where the CP-even Higgs boson with the mass of 125 GeV has the same tree-level couplings as the SM.
The alignment limit in two Higgs doublet models (2HDMs) was discussed in e.g., Refs. [3]}, [4]}, and, in the context of 3HDM, the analytical condition for the limit was systematically derived  in Ref. [5]}.
Symmetries for the Higgs potential that naturally lead to the alignment limit was discussed in Ref. [6]}.
